JEE Main 2014MathematicsBinomial TheoremMediumMCQ

JEE Main 2014 — Binomial Theorem Question with Solution

JEE Main 2014 (06 Apr)

Question

If the coefficients of x3 and x4 in the expansion of 1+ax+bx21-2x18 in powers of x are both zero, then a,b is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B 1 6 ,  2 7 2 3

Step-by-step explanation

We have, 1+ax+bx21-2x18=a0+a1x+a2x2+.......
=1+ax+bx21-18C1·2x+18C2·22x2+.....18C182x18

⇒a3=-18C3×8+18C2×4a-36b

⇒a4=18C4×16-18C3×8a+18C2×4×b

102a-6b=1088  ...i

64a-6b=480  ...ii

Solution of the above two equation gives.

a=16
b = 2 7 2 3

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About this question

This is a previous-year question from JEE Main 2014, covering the Binomial Theorem chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.